Question: (10 points)

Let D = days of the week {M, T, W, R, F},

E = {Brian (B), Jim (J), Karen (K)} be the employees of a tutoring center at a University and let

U = {Courses the tutoring center needs tutors for} = {Calculus I (I), Calculus II (II), Calculus III (III), Computers I (C₁), Computers II (C₂), Precalculus (P)}.

We define the relation R from D into E by d R e, if employee e is scheduled to work on day d. We also define S from E into U by e r u, if employee e is capable of tutoring students in course u.

If you are given M_R = \[\begin{aligned} & \text{ }\begin{matrix} \text{B} & \text{J} & \text{K} \\ \end{matrix} \\ & \begin{matrix} \text{M} \\
\text{T} \\
W \\
R \\
F \\
\end{matrix}\left[ \begin{aligned} & 1\text{ 0 1} \\ & \text{0 1 1} \\ & \text{1 0 1} \\ & \text{0 1 0} \\ & \text{1 1 0} \\ \end{aligned} \right] \\ \end{aligned}\] and M_S = \[\begin{aligned}

& \text{ I II III }{{\text{C}}_{\text{1}}}\text{ }{{\text{C}}_{\text{2}}}\text{ P} \\

& \begin{matrix}

\text{B} \\
\text{J} \\
\text{K} \\
\end{matrix}\left[ \begin{aligned} & \text{0 1 1 0 0 1} \\ & \text{1 1 0 1 0 1} \\ & \text{0 1 0 0 1 1} \\ \end{aligned} \right] \\ \end{aligned}\]

(a) Interpret the above matrices with respect to the above relations.

(b) Compute \({{\text{M}}_{\text{S}\circ \text{R}}}\), and use the matrix \({{\text{M}}_{\text{S}\circ \text{R}}}\) to determine which courses will have tutors available on which days.

(c) Multiply the above matrices using regular arithmetic. Can you interpret this result?